Once I get a bunch of potential points within the rect of a poly, I should find the 4 outermost points in each dimension. Once I determine those four definitively, all points within those 4 would be also within that poly, and I wouldn't have to do the checks for them.

If I understand you correctly, then given the polygon below and the four points marked as dots ("."), wouldn't that method determine that the point marked with an "x" is inside the polygon?

If all of your polygons were guananteed to have internal angles > 90 degrees that might work, but you only said that they were "irregular". I had a similar idea yesterday (except mine was finding the maximum internal bounding rectangle for the polygon rather than using the query points themselves), and discarded it for this reason. :-)